How do you plan to record the grade a student has for each of his/her classes? What is the difference between class and course?
I feel a lot of your relationships are backwards. For example, student and major. In your design, each major can only have one student. Also, each class can only have one student and each field can only have one student.
Again, I would recommend starting with the design I gave you; once you have that set up correctly, then work on adding the additional tables you didn't mention in your original post.